Julia is the only thing in Winston's life that has ever been beautiful, happy, and fulfilling. He works in a job that is a lie, essentially, lives in a society that won't allow him to be himself and drives him to paranoia, and had a lifeless and loveless marriage. His environment and surroundings were dank, dreary and broken, and even food was rationed and gross. Basically,his life was joyless, monotonous, miserable and without any glimmer of fulfillment. Then, Julia came onto the scene. She provided him with unconditional love, physical stimulation and satisfaction, and most important of all, complete and total validation of his hatred for the Party. He always wondered if he was the only one who hated the party, and his discomfort with that and wonder about it kept him in a constant state of anxiety and insecurity. But, Julia helps him to realize that he is not alone, that there are reasons to hate the party, and that he isn't insane for hating it. She teaches him how to rebel, and even opens his eyes to things he had never considered before. She allows him to be confident again, and to bear his life. She gives him courage, purpose and strength.
That's it in a nutshell for you--Julia gives Winston life back again, and helps him to feel like a strong person. She gives him hope, which is a very important thing in their world. I hope that those thoughts helped; good luck!
Usually, you would think that she would be important to him for sexual reasons or because he loves her. But that is not really what's going on in this book, in my opinion. To me, Julia is important to Winston because she represents a way to get back at or to oppose the Party.
You can see this from his reaction to her saying that she has had sex with lots of Party members. If he were in love, he probably wouldn't have been happy about that. But instead, he is really happy because it shows that she hates the Party also and will be a willing partner in doing things that will undermine the Party and the system it has set up.